Method and system for damping sloshing molten metal

ABSTRACT

The disclosed method is a control to suppress sloshing in a ladle of a pouring device and a mold caused by their movements. A plurality of flasks, each of which contains a conveyed mold, is arranged linearly between an electric pusher-cylinder and an electric cushion-cylinder. In the method, a first natural frequency of the molten metal in the ladle is calculated based on a predetermined relationship between the weight and the natural frequency for the molten metal in the ladle, and the measured weight of the molten metal in said ladle. Also, a second natural frequency of the molten metal in said mold is calculated based on a predetermined relationship between the weight and the natural frequency for the molten metal in the mold, and the measured weight of the molten metal in the mold. The first and second natural frequencies are entered in a filtering circuit to modify a velocity waveform of the movement of conveying the flasks such that the modified velocity waveform does not include the first and second natural frequencies. The electric pusher-cylinder and the electric cushion-cylinder are driven such that the velocity waveform of the movement of conveying the flasks is said modified velocity waveform.

FIELD OF THE INVENTION

The present invention generally relates to a control for a casting line.In particular the present invention relates to a method and a system fordamping the sloshing that occurs in molten metal in a ladle and a moldin the casting line.

BACKGROUND OF THE INVENTION

Patent publication 1, listed below, discloses one example of theconventional casting line in which a conveying line for conveying moldsis provided with an encoder to detect the rate of feeding a mold.Responding to the detection signal of the encoder, a pouring devicetracks, and synchronizes with the conveying mold, such that the pouringdevice moves to the proper position, i.e., where a ladle of the pouringdevice pours molten metal into the mold.

Reference of Prior-Art Document

-   Patent Citation 1: Japanese Patent No. 3113950 (Isuzu Manufacturing    Co., Ltd.)

In such a conventional casting line, because cylinders push out and thusconvey a flask that contains the mold and the pouring device, thevelocity waveform of the flask or the pouring device has a waveform thatis generally trapezoidal when it is moved for conveying. This involvessloshing the molten metal in the ladle of the pouring device and themold to cause the fluid level of the molten metal to ripple. As aresult, a casting piece may contain a sand inclusion or a casting finthat adversely affects the quality of the cast product.

Accordingly, there is a need for a method and a system for dampingsloshing that occurs in molten metal in a ladle and a mold in a castingline where a process of pouring is automatic.

SUMMARY OF THE INVENTION

A first aspect of the present invention provides a method and a systemof suppressing sloshing in a casting line that includes a conveying linein which an electric pusher-cylinder is located at one end of theconveying line for intermittently pushing out a plurality of flasks,each containing a mold, one by one. It also includes an electriccushion-cylinder that is located at the other end of the conveying linesuch that it is opposed to the electric pusher-cylinder so as to receiveand cushion a group of the pushed flasks such that the conveying lineconveys the plurality of flasks, which are arranged linearly between theelectric pusher-cylinder and the electric cushion-cylinder; and anautomatic pouring device that has a ladle for containing molten metaland that can be moved in synchronization with the flask on the conveyingline, to pour the molten metal into the mold by tilting the ladle. Themethod and system control the electric pusher-cylinder and the electriccushion-cylinder using a controller having filtering means such that thesloshing that occurs in the molten metal is suppressed when the ladleand the mold move a distance that corresponds to one flask.

The method comprises: calculating a first natural frequency of themolten metal in the ladle based on a predetermined relationship betweenthe weight and the natural frequency for the molten metal in the ladle,and the measured weight of the molten metal in the ladle, andcalculating a second natural frequency of the molten metal in the moldbased on a predetermined relationship between the weight and the naturalfrequency for the molten metal in the mold, and the measured weight ofthe molten metal in the mold; entering the first and second naturalfrequencies in the filtering means to modify a velocity waveform of themovement of conveying the flasks such that the modified velocitywaveform does not include the first and second natural frequencies; anddriving the electric pusher-cylinder and the electric cushion-cylindersuch that the velocity waveform of the movement of conveying the flasksis the modified velocity waveform.

The system comprises: a first weight-calculation means for calculatingthe weight of the molten metal in the ladle; a second weight-calculationmeans for calculating a second natural frequency of the molten metal inthe mold; a first natural frequency-calculation means for calculating afirst natural frequency based on a predetermined relationship betweenthe weight and the natural frequency for the molten metal in the ladle,and the calculated weight of the molten metal in the ladle by the firstweight-calculation means; a second natural frequency-calculation meansfor calculating a second natural frequency based on a predeterminedrelationship between the weight and the natural frequency for the moltenmetal in the mold, and the calculated weight of the molten metal in themold by the second weight-calculation means; a filtering means formodifying a velocity waveform of the movement of conveying the flasks onthe conveying line such that the modified velocity waveform does notinclude the first and second natural frequencies calculated by the firstand second natural frequency-calculation means; and an instructing meansfor providing operating instructions to the electric pusher-cylinder,the electric cushion-cylinder, and the automatic pouring device, basedon the modified velocity waveform.

A second aspect of the present invention provides a method and a systemof suppressing sloshing in a casting line, wherein the casting lineincludes: a conveying line in which an electric pusher-cylinder islocated at one end of the conveying line for intermittently pushing outa plurality of flasks that each contains a mold, one by one, and anelectric cushion-cylinder that is located at the other end of theconveying line that is opposed to the electric pusher-cylinder toreceive and cushion a group of the pushed flasks such that the conveyingline conveys the plurality of flasks that is arranged linearly betweenthe electric pusher-cylinder and the electric cushion-cylinder; anautomatic pouring device that has a ladle for containing molten metaland that can be moved in synchronization with the flask on the conveyingline, to pour the molten metal into the mold by tilting the ladle;driving means for driving the electric pusher-cylinder, the electriccushion-cylinder, and the automatic pouring device along the conveyeddirection of the flasks; controlling means for controlling the drivingmeans; and instructing means for providing operating instructions forthe electric pusher-cylinder, the electric cushion-cylinder, and theautomatic pouring device to the driving means through the controllingmeans.

The method and the system control the casting line using a controllerhaving filtering means, based on a feedforward control program such thatthe sloshing that occurs in the molten metal is suppressed when theladle and the mold move a distance corresponding to one flask.

The method of the second aspect comprises: calculating a first naturalfrequency of the molten metal in the ladle based on a predeterminedrelationship between the weight and the natural frequency for the moltenmetal in the ladle, and the measured weight of the molten metal in theladle, and calculating a second natural frequency of the molten metal inthe mold based on a predetermined relationship between the weight andthe natural frequency for the molten metal in the mold, and the measuredweight of the molten metal in the mold; under the first naturalfrequency, the second natural frequency, and parameters on thecontrolling means that are preliminarily calculated such that they donot exceed the capacities of the driving means and that are stored,removing components that are located near the first and secondfrequencies from the operating instructions, in which the maximum valueof at least one of a velocity of the movement, an acceleration of themovement, and a jerk of the ladle and the mold is restricted, by thefiltering means using the stored parameters, wherein the components tobe removed are decided based on a simulation using a model representingthe characteristics of the casting line to repeatedly calculate thecomponents by the following equation (1) or (2), while gradually varyingfiltering parameters ai(f), bj(f) that are parameterized by a resonancefrequency f that are successively calculated from the molten metal inthe ladle and the mold; and entering the operating instructions, inwhich the components located near the first and second frequencies havebeen removed, in the controlling means based on only the feedforwardcontrolling program, to operate the driving means based on only thefeedforward controlling program without using a feedback controlprogram.

$\begin{matrix}{\lbrack {{Math}.\mspace{14mu} 1} \rbrack \mspace{644mu}} & \; \\{{{y(t)} = {{{b_{0}(f)}{x(t)}} + {{b_{1}(f)}{x( {t - 1} )}} + {{b_{2}(f)}{x( {t - 2} )}} + \ldots - {{a_{1}(f)}{y( {t - 1} )}} - {{a_{2}(f)}{y( {t - 2} )}} - \ldots}}{{y(t)} = {{\sum\limits_{j = 0}^{m}\; {{b_{j}(f)}{x( {t - j} )}}} - {\sum\limits_{i = 1}^{n}\; {{a_{1}(f)}{y( {t - i} )}}}}}} & (1)\end{matrix}$

where x(t-j) is a time-series data that is input before j controllingcycles, and y (t-i) are a time-series data that are output before icontrolling cycles.

$\begin{matrix}{\lbrack {{Math}.\mspace{14mu} 2} \rbrack \mspace{644mu}} & \; \\\begin{matrix}{{F(S)} = \frac{Y(S)}{X(S)}} \\{= \frac{{{b_{0}(f)}S^{0}} + {{b_{1}(f)}S^{1}} + {{b_{2}(f)}S^{2}} + \ldots}{{{a_{0}(f)}S^{0}} + {{a_{1}(f)}S^{1}} + {{a_{2}(f)}S^{2}} + \ldots}} \\{= \frac{\sum\limits_{j = 0}^{m}\; {{b_{j}(f)}S^{j}}}{\sum\limits_{i = 0}^{n}\; {{a_{i}(f)}S^{i}}}}\end{matrix} & (2)\end{matrix}$

where S is the Laplace operator, and equation (1) can be derived byapplying a Z transformation on the transfer function of the filter thatis expressed as equation (2).

As stated above, restricting the maximum value of at least one of avelocity of the movement, an acceleration of the movement, and a jerk ofthe movement, of the ladle and the mold can ensure that the drivingmeans of the casting line prevents an excess, in particular, of theacceleration of the automatic pouring device and the flasks. Further,removing the components of the resonance frequencies by filtering theoperating instructions to convey the flasks can prevent the efficiencyof the control means of the driving means of the casting line fromsignificant degradation, even if the detected weights of the moltenmetal in the ladle and the mold involves a detected error.

The system of the second aspect comprises: a first weight-calculationmeans for calculating the weight of the molten metal in the ladle; asecond weight-calculation means for calculating a second naturalfrequency of the molten metal in the mold; a first naturalfrequency-calculation means for calculating a first natural frequencybased on a predetermined relationship between the weight and the naturalfrequency for the molten metal in the ladle, and the calculated weightof the molten metal in the ladle by the first weight-calculation means;a second natural frequency-calculation means for calculating a secondnatural frequency based on a predetermined relationship between theweight and the natural frequency for the molten metal in the mold, andthe calculated weight of the molten metal in the mold by the secondweight-calculation means; an instructing means for providing operatinginstructions based on a feedforward program for operations of theelectric pusher-cylinder, the electric cushion-cylinder, and theautomatic pouring device, to the driving means through the controllingmeans; a parameter calculation means for preliminarily calculating theparameters of the controlling means such that the calculated parametersdo not exceed the capacity of the driving means; a stored means forreceiving and storing the calculated parameters from the parametercalculation means; a restriction means for restricting the maximum valueof at least one of a velocity of the movement, an acceleration of themovement, and a jerk of the automatic pouring device and the mold; afiltering means for receiving the first and second resonance frequenciesfrom the first and second frequency-calculation means, and for removingcomponents that are located near adjacent to the first and secondfrequencies from the operating instructions, in which the maximum valueis restricted by the restriction means, using the stored parameters fromthe stored means, wherein the components to be removed are decided basedon a simulation using a model representing the characteristics of thecasting line to repeatedly calculate the components, under the storedparameters, by the above equation (1) or (2), while gradually varyingfiltering parameters ai(f), bj(f) that are parameterized by a resonancefrequency f that are successively calculated from the molten metal inthe ladle and the mold, and wherein the instructing means provides thecontrolling means with the operating instructions in which thecomponents located near the first and second frequencies are removedsuch that the controlling means carries out the controls based on onlythe feedforward controlling program, without using a feedback controlprogram.

As used herein, the term “filtering means” refers to a circuit or itspartial configuration that includes a pair of an input terminal and anoutput terminal with a transfer function therebetween that has afrequency response.

As used herein, the term “feedforward control” refers to way to controla manipulative variable to be applied to a controlled object to apredetermined value such that output value is a target value. Thefeedforward control may provide a highly efficient control if aninput-output relation and a disturbance, for example, to the controlledobject, are definite.

As used herein, the term “jerk” refers to a rate of deviation in anacceleration relative to the time.

The forgoing and the other features and objects of the present inventionwill also be obvious from the following descriptions by referring to theaccompanied drawing. Note that the various embodiments of the presentinvention are not intended to be limited to the illustrated arrangementsand means.

BRIEF DESCRIPTION OF THE DRAWING

FIG. 1 is a schematic block diagram of one embodiment of the castingequipment to which the present invention is applied.

EMBODIMENT OF THE INVENTION The First Embodiment

FIG. 1 shows casting equipment to which the method and the system of thepresent invention is applied. The casting equipment includes a castingline in which a conveying line A conveys a plurality of flasks. Eachcontains a mold Y to a conveyed direction designated by an arrow X,arranged linearly, such that the casting line carries out castingprocesses using the conveyed flasks. For the ease of understanding theillustration, each flask is schematically shown as a contour of thecorresponding Y. Arranged on the casting line are an electricpusher-cylinder B, an electric cushion-cylinder C, and an automaticpouring device D. The electric pusher-cylinder B is located at one endof the conveying line A for the flasks to intermittently push out theplurality of flasks one by one. The electric cushion-cylinder C islocated at the other end of the conveying line A that is opposed to theelectric pusher-cylinder B to receive and cushion a group of the pushedflasks. The automatic pouring device D, which has a ladle Z forcontaining molten metal, can be moved in the direction X insynchronization with the flask on the conveying line A, to pour themolten metal into the mold by tilting the ladle Z. The automatic pouringdevice D is provided with a driving motor (driving means), not shown, tomove it in the direction X. Although the automatic pouring device D isalso provided with a plurality of motors (not shown) to let the ladle Zmove vertically, forward and backwards, and tilt, explanations for thesemotors to move the ladle Z are omitted. The casting equipment is alsoprovided with a system to control a controller having a filter circuit,using a program to control the operations of the electricpusher-cylinder B, the electric cushion-cylinder C, and the automaticpouring device D, in the casting line.

On the electric pusher-cylinder B and the electric cushion-cylinder C,induction motors (driving means) B1 and C1 for driving the respectiveball screws are mounted as driving motors to move them in the directionX. The induction motors B1 and C1 are electrically connected to a firstservo controller (controlling means) B3 and a second servo controller(controlling means) C3 through inverters B2 and C2 that can control theposition by entering data on a pulse string.

The control system includes, besides the first and second servocontrollers B3 and C3 described above, a control unit J for theautomatic pouring device D to control the X driving motor to drive theautomatic pouring device D in the X direction (and the driving motors todrive the ladle Z) and a control device K for the conveying line of theflasks to control the first and second servo controllers B3 and C3. Thecontrol system also includes the following functions: a firstweight-calculating means for calculating the weight of the molten metalin the ladle Z; a second weight calculating means for calculating theweight of the molten metal in the mold Y; a first natural frequencycalculating means for calculating the natural frequency (the firstnatural frequency) of the molten metal in the ladle Z based on apredetermined relationship between the weight and the natural frequencyfor the molten metal in the ladle Z, and the calculated weight of themolten metal in the ladle Z from the first weight-calculating means; asecond natural frequency calculating means for calculating the naturalfrequency (the second natural frequency) of the molten metal in the moldY based on a predetermined relationship between the weight and thenatural frequency for the molten metal in the mold Y, and the calculatedweight of the molten metal in the mold Y from the secondweight-calculating means; an instructing means for providing operatinginstructions to the electrical pusher-cylinder B, the electricalcushion-cylinder C, and the automatic pouring device D, based on thecontrol program; and a filtering means for modifying a velocity waveformof a conveying motion of the flask to be targeted such that the castingline is operated by the modified velocity waveform that does not includethe calculated natural frequencies of the molten metal in the ladle orin the mold from the first and second weight-calculating means.

The first servo controller B3 may comprise a central processing unit(CPU) B3 a, a pulse output device B3 b, I/O B3 c, a communication deviceB3 d, a servo I/O B3 e, and a counter B3 f. The second servo controllerC3 may, like the first servo controller B3, comprise a centralprocessing unit (CPU) C3 a, a pulse output device C3 b, I/O C3 c, acommunication device C3 d, a servo I/O C3 e, and a counter C3 f.

The first servo controller B3 and the second servo controller C3 areconnected to a communication device K2 of the control device K of theconveying line through communication devices B3 d and C3 d, whichtransmit and receive digital data, to acquire data on the weights of themolten metal in the control unit K for the conveying line.

The control unit J of the automatic pouring device is electricallyconnected to the control device K of the conveying line such that thecontrol unit J transmits signals indicating the weights of the moltenmetal in the ladle Z and mold Y to the control device K through the linkcommunication devices J3 and K3. The control unit J also includes aprogrammable logic controller (PLC) J4 to control the X driving motor ofthe automatic pouring device D.

The first and the second servo controller B3 and C3 transmit apositional command (a signal) of a pulse string to the inverters B2 andC2 to drive the induction motors B1 and C1. Controlling the torques,speeds, and positions of these motors, is carried out by the invertersB2 and C2.

Attached to the automatic pouring device D is a load cell G to measurethe weight of the molten metal in the ladle Z. The load cell G iselectrically connected to an analog input unit J1 of the control unit Jof the automatic pouring device through an amplifier H.

The function of the casting equipment constructed as described abovewill now be explained. The weight of the molten metal in the ladle Z isdetected by the load cell G, and to measure it, it is then input intothe analog input unit J1 of the control unit J of the automatic pouringdevice. The molten metal in the ladle Z of the automatic pouring deviceD is then poured into the mold Y. The measured weight of the moltenmetal in the ladle Z and the reduced weight of the molten metal in themold Y that is calculated from the former are then provided in thecontrol device K of the conveying line, to retrieve the naturalfrequency (the first natural frequency) of the molten metal in the ladleZ and the natural frequency (the second natural frequency) of the moltenmetal in the mold Y.

The electric cushion-cylinder C is positioned at a predetermined setposition in readiness. When the first and the second servo controllersB3 and C3 detect a signal indicating that the flask to be conveyed fromthe programmable logic controller (PLC) K4 of the control device K ofthe conveying line, the electric pusher-cylinder B is first extended ata low speed to secure the group of the flasks on the conveying lineentirely in the sandwiched relation between the electric pusher-cylinderB and the electrical cushion-cylinder C. Then the electricpusher-cylinder B is extended, while the electric cushion-cylinder C iscontracted in the same velocity waveform of the electric pusher-cylinderB, to convey the flasks such that the group of the flasks moves in the Xdirection by a distance corresponding to one flask. At the same time,the automatic pouring device D pours the molten metal into the mold Y,while the automatic pouring device D is moved in the X direction by thedistance corresponding to one flask. In such a rapid motion, a sloshingsuppression control is carried out to prevent the molten metal in theladle Z and the mold Y from the sloshing, as described below.

Both the calculated natural frequency of the molten metal in the ladle Zand the calculated natural frequency of the molten metal in the mold Yare input into the filtering means to modify the velocity waveform ofthe conveying motion of the flasks on the conveying line, to provide aversion of it that is modified without including these two naturalfrequencies. Both the electric pusher-cylinder B and the electricalcushion-cylinder C are then driven such that the velocity waveform ofthe conveying motion of the flasks is in the modified version. Thus, thesloshing that occurs in the molten metal in the ladle Z and the mold Ycan be accurately suppressed when the ladle Z and the flasks are movedby a distance corresponding to one flask.

The control unit J of the automatic pouring device D causes the secondservo controller C3 to transmit the signals indicating that the flasksare conveyed while the automatic pouring device D pours the moltenmetal. The transmitted signal is input into the counter J2 to beconverted to positional data. The X driving motor of the automaticpouring device D is then driven to follow the positional command basedon the converted positional data to move the automatic pouring device Din the X direction such that it follows the conveyed motion of theflasks.

Because the molten metal in the ladle Z and the mold Y has a complicatedshape and thus it is difficult to accurately calculate the respectivenatural frequencies, a relationship between the weights of the moltenmetal in the ladle Z and natural frequencies that are derived based on amethod to estimate the natural frequencies, described below, ispreliminarily established as parameters. The method for determining thenatural frequencies includes, for example, a derivation based on fluidanalysis software, or an estimation based on the magnitude of theamplitude of the vibrations when the molten metal is actually vibrated.This derivation is made while the frequencies are varied. One examplethat may be used as the fluid analysis software is three-dimensionalthermo-fluid analysis software that can calculate with a high accuracy acomplicated and unstable behavior of fluid that involves nonlinearbehavior or a large deformation behavior.

Although, as described above, the inverter control of the servocontrollers in this embodiment is based on the positional control by theoutput of the pulse string, such a control may be carried out at theside of the servo controllers by configuring control loops forvelocities and positions. The induction motors B1, C1 and the invertersB2, C2 may be replaced by servomotors and servo amplifiers.

The Second Embodiment

The same as the first embodiment, the control system in the secondembodiment includes the first servo controller B3, the second servocontroller C3, the control unit J of the automatic pouring device D, andthe control device K of the conveying line, as described above. Thecontrol system in the second embodiment also includes an arrangement forcontrolling the suppression of sloshing. This arrangement includes, thesame as with the first embodiment, a first weight-calculating means forcalculating the weight of the molten metal in the ladle Z; a secondweight calculating means for calculating a weight of molten metal in themold Y; a first natural frequency-calculation means for calculating thenatural frequency (the first natural frequency) of the molten metal inthe ladle Z based on a predetermined relationship between the weight andthe natural frequency for the molten metal in the ladle Z, and thecalculated weight of the molten metal in the ladle Z from the firstweight-calculating means; a second natural frequency-calculation meansfor calculating the natural frequency (the second natural frequency) ofthe molten metal in the mold Y based on a predetermined relationshipbetween the weight and the natural frequency for the molten metal in themold Y, and the calculated weight of the molten metal in the mold Y fromthe second weight-calculating means. However, the arrangement forcontrolling the suppression of sloshing in the second embodiment,instead of being that of the instructing means and the filtering meansof the first embodiment, includes the following instructing means,parameter calculation means for calculating parameters, storing meansfor storing parameters, restricting means for restricting the maximalvalue, and filtering means. In this embodiment, the instructing meansprovides operating instructions based on a forward control program forthe operation of the casting line. The means to calculate parameterspreliminarily calculates the parameters of the controllers (i.e., thefirst servo controller B3, the second servo controller C3, and thecontrol unit J of the automatic pouring device D) of the driving devicesfor the X direction (i.e., the induction motor B1 of the electricpusher-cylinder B, the induction motor C1 of the electriccushion-cylinder C, and the X driving motor of the automatic pouringdevice D) of the casting line such that the calculated parameters do notexceed the capacities of these driving devices for the X direction. Thestoring means receives the parameters from the calculating means andstores them. In line with the stored parameters given by the storingmeans, the restricting means limits the maximum value in at least one ofa velocity of the movement, an acceleration of the movement, and a jerkof the movement of the automatic pouring device and the flasks in theoperating instructions for the casting line from the instructing means.In line with the stored parameters given by the storing means, thefiltering means receives data on the first and second resonancefrequencies from the first and second resonance frequency-calculationmeans, and thus removes components located near them from the operatinginstructions in which the maximum value is restricted by the restrictingmeans.

Removing the components located near the first and second resonancefrequencies is carried out using filtering parameters that arepreliminarily stored by simulating a model representing thecharacteristics of the casting line to repeatedly calculate thecomponents by the following equation (1) or (2), while gradually varyingthe filtering parameters ai(f), bj(f). Further, the instructing meansprovides the operating instructions in which the components located nearthe first and second resonance frequencies are removed, by the filteringmean, to the driving devices for the X direction through thesecontrollers. These controllers drive the driving devices for the Xdirection based on just the feedforward control program, without thefeedback program. The construction for carrying out the control ofsuppression of sloshing can be implemented by a computer.

$\begin{matrix}{\lbrack {{Math}.\mspace{14mu} 3} \rbrack \mspace{644mu}} & \; \\{{{y(t)} = {{{b_{0}(f)}{x(t)}} + {{b_{1}(f)}{x( {t - 1} )}} + {{b_{2}(f)}{x( {t - 2} )}} + \ldots - {{a_{1}(f)}{y( {t - 1} )}} - {{a_{2}(f)}{y( {t - 2} )}} - \ldots}}{{y(t)} = {{\sum\limits_{j = 0}^{m}\; {{b_{j}(f)}{x( {t - j} )}}} - {\sum\limits_{i = 1}^{n}\; {{a_{1}(f)}{y( {t - i} )}}}}}} & (1)\end{matrix}$

where ai(f), bj(f) are filtering parameters that are parameterized fromresonance frequencies f sequentially calculated from the molten metal inthe ladle and the mold, x(t-j) is time-series data that is input beforej controlling cycles, and y (t-i) denotes time-series data that areoutput before i controlling cycles.

$\begin{matrix}{\lbrack {{Math}.\mspace{14mu} 4} \rbrack \mspace{644mu}} & \; \\\begin{matrix}{{F(S)} = \frac{Y(S)}{X(S)}} \\{= \frac{{{b_{0}(f)}S^{0}} + {{b_{1}(f)}S^{1}} + {{b_{2}(f)}S^{2}} + \ldots}{{{a_{0}(f)}S^{0}} + {{a_{1}(f)}S^{1}} + {{a_{2}(f)}S^{2}} + \ldots}} \\{= \frac{\sum\limits_{j = 0}^{m}\; {{b_{j}(f)}S^{j}}}{\sum\limits_{i = 0}^{n}\; {{a_{i}(f)}S^{i}}}}\end{matrix} & (2)\end{matrix}$

where equation (1) can be derived by applying a Z transformation to thetransfer function of the filter that is expressed as equation (2), and Sis the Laplace operator.

In the second embodiment, the weight of the molten metal in the ladle isentered in the first resonance frequency-calculation means to calculatethe resonance frequency of the molten metal in the ladle, while theweight of the molten metal in the mold is entered in the secondresonance frequency-calculation means to calculate the resonancefrequency of the molten metal in the mold. These two calculatedresonance frequencies are entered in the filter.

Meanwhile, the instructing means provides the operating instructions tothe restricting means. The restricting means then reads out the storedparameters on the controllers of the driving devices for the X directionin the casting line from the parameter storing means, while therestricting means limits the maximum value in at least one of thevelocity of the movement, the acceleration of the movement, and the jerkof the movement of the automatic pouring device and the flasks in theoperating instructions from the instructing means such that thecalculated parameters do not exceed the capacities of these drivingdevices for the X direction. The results are provided to the filter.

The filtering means reads out the stored parameters on the controllersof the driving devices for the X direction in the casting line that donot exceed the capacities of these driving devices from the parameterstoring means. The filtering means filters the operating instructions tobe provided to the driving devices in the X direction in which themaximum value is restricted in at least one of the velocity of themovement, the moving acceleration, and the moving jerk of the automaticpouring device and the flasks in line with the two resonance frequenciessequentially calculated from the molten metal in the ladle and the mold,to remove from the operating instructions the components located nearthe first and second resonance frequencies. The resulting filteringoperating instructions are entered in the driving devices for the Xdirection in the casting line through their controllers. Thus, anysloshing that has occurred in the molten metal in the ladle Z and themold Y can be suppressed when the ladle Z and the flasks are moved by adistance corresponding to one flask.

The calculation by the filtering means is executed based on theprinciple as discussed below. Namely, assuming that x (t) is time-seriesdata to be input in the filtering means, and y (t) is time-series dataoutput from the filtering means, a filter to be applied to thetime-series data is expressed by equation (1).

$\begin{matrix}{\lbrack {{Math}.\mspace{14mu} 5} \rbrack \mspace{644mu}} & \; \\{{{y(t)} = {{{b_{0}(f)}{x(t)}} + {{b_{1}(f)}{x( {t - 1} )}} + {{b_{2}(f)}{x( {t - 2} )}} + \ldots - {{a_{1}(f)}{y( {t - 1} )}} - {{a_{2}(f)}{y( {t - 2} )}} - \ldots}}{{y(t)} = {{\sum\limits_{j = 0}^{m}\; {{b_{j}(f)}{x( {t - j} )}}} - {\sum\limits_{i = 1}^{n}\; {{a_{1}(f)}{y( {t - i} )}}}}}} & (1)\end{matrix}$

where, ai(f), bj(f) are parameters that are parameterized from tworesonance frequencies f sequentially calculated from the molten metal inthe ladle Z and the mold Y.

Further, x(t-j) is time-series data that are input before j controllingcycles, and y (t-i) is time-series data that are output before icontrolling cycles.

Although the number of items m and n can be appropriately determinedbased on the construction of the filter, they should be preliminarydecided. For example, m=0 and n=1 if the filter is a primary low-pathfilter, m=0 and n=1 if it is a secondary low-path filter, and m=2 andn=2 if it is a notch filter, can be preliminarily decided. These decidednumbers of items m and n are entered in the parameter storing means andthe parameter calculation means.

The parameters ai(f), bj(f) should be preliminary calculated and decidedusing the parameter calculation means by simulations using a modelrepresenting the characteristics of the casting line to repeatedlycalculate them, while their values are being gradually varied.

To calculate these parameters, the constraining conditions in theoperating instructions to be provided to the driving devices for the Xdirection in the casting line are as follows: the maximum velocity inthe operating instructions should not exceed the maximum velocities ofthe electrical pusher-cylinder B and the electrical cushion-cylinder C,each maximum value of the maximum velocities of them should not exceedthe restrictions on the maximum value on the driving devices for the Xdirection, and the time of the movements of the ladle Z and the flasksbecomes the shortest.

Equation (1) can be derived by applying a Z transformation to thetransfer function of the filter that is expressed as the followingequation (2).

$\begin{matrix}{\lbrack {{Math}.\mspace{14mu} 6} \rbrack \mspace{644mu}} & \; \\\begin{matrix}{{F(S)} = \frac{Y(S)}{X(S)}} \\{= \frac{{{b_{0}(f)}S^{0}} + {{b_{1}(f)}S^{1}} + {{b_{2}(f)}S^{2}} + \ldots}{{{a_{0}(f)}S^{0}} + {{a_{1}(f)}S^{1}} + {{a_{2}(f)}S^{2}} + \ldots}} \\{= \frac{\sum\limits_{j = 0}^{m}\; {{b_{j}(f)}S^{j}}}{\sum\limits_{i = 0}^{n}\; {{a_{i}(f)}S^{i}}}}\end{matrix} & (2)\end{matrix}$

where S is the Laplace operator.

In the second embodiment, the induction motors B1, C1 and the invertersB2, C2 of the electric pusher-cylinder B and the electriccushion-cylinder C may also be replaced by servomotors and servoamplifiers.

The computer to use for the embodiments of the present invention mayinclude a central processing unit (CPU), an input device, a display, amemory, and any other circuit that is able to perform the functionsdescribed herein.

The computer also may include a storage device that may include a harddisk drive, an optical disk drive, a floppy disk drive, etc. The storagedevice may use other similar means to load a computer program or otherinstructions to the computer.

The computer program, when loaded and executed, controls the computersuch that it carries out the methods described herein. A computerreadable storage media that stores the computer program may include anyvolatile or non-volatile storage device.

Because the above embodiments are not intended to limit the presentinvention to any specific embodiment, it will be appreciated thatvarious modifications and variations may be embodied without departingfrom the spirit and the scope of the present invention.

1. A method of suppressing sloshing in a casting line, wherein saidcasting line includes: a conveying line in which an electricpusher-cylinder is located at one end of the conveying line forintermittently pushing out a plurality of flasks, wherein each flaskcontains a mold, one by one, and an electric cushion-cylinder is locatedat the other end of said conveying line and opposed to said electricpusher-cylinder to receive and cushion a group of said pushed flaskssuch that said conveying line that conveys said plurality of flasks isarranged linearly between said electric pusher-cylinder and saidelectric cushion-cylinder; and an automatic pouring device that has aladle for containing molten metal and that can be moved insynchronization with the flask on the conveying line, to pour the moltenmetal into the mold by tilting said ladle; said method controlling saidelectric pusher-cylinder and said electric cushion-cylinder by using acontroller having filtering means such that the sloshing that occurs inthe molten metal is suppressed when said ladle and said mold move by adistance corresponding to one flask, said method comprising: calculatinga first natural frequency of the molten metal in said ladle based on apredetermined relationship between the weight and the natural frequencyfor the molten metal in said ladle, and the measured weight of themolten metal in said ladle, and calculating a second natural frequencyof the molten metal in said mold based on a predetermined relationshipbetween the weight and the natural frequency for the molten metal insaid mold, and the measured weight of the molten metal in said mold;entering the first and second natural frequencies in said filteringmeans to modify a velocity waveform of the movement of conveying saidflasks such that the modified velocity waveform does not include thefirst and second natural frequencies; driving said electricpusher-cylinder and said electric cushion-cylinder such that thevelocity waveform of the movement of conveying said flasks is saidmodified velocity waveform.
 2. A system of suppressing sloshing in acasting line, wherein said casting line includes: a conveying line inwhich an electric pusher-cylinder is located at one end of the conveyingline for intermittently pushing out a plurality of flasks, wherein eachcontains a mold, one by one, and an electric cushion-cylinder is locatedat the other end of said conveying line and is opposed to said electricpusher-cylinder to receive and cushion a group of said pushed flaskssuch that said conveying line that conveys said plurality of flasks isarranged linearly between said electric pusher-cylinder and saidelectric cushion-cylinder; and an automatic pouring device that has aladle for containing molten metal and that can be moved insynchronization with the flask on the conveying line, to pour the moltenmetal into the mold by tilting said ladle; wherein said system thatcontrols said casting line such that the sloshing that occurs in themolten metal in said ladle and said mold is suppressed when said ladleand said mold move by a distance corresponding to one flask; said systemcomprising: a first weight-calculation means for calculating the weightof the molten metal in said ladle; a second weight-calculation means forcalculating a second natural frequency of the molten metal in said mold;a first natural frequency-calculation means for calculating a firstnatural frequency based on a predetermined relationship between theweight and the natural frequency for the molten metal in said ladle, andthe calculated weight of the molten metal in said ladle by said firstweight-calculation means; a second natural frequency-calculation meansfor calculating a second natural frequency based on a predeterminedrelationship between the weight and the natural frequency for the moltenmetal in said mold, and the calculated weight of the molten metal insaid mold by said second weight-calculation means; filtering means formodifying a velocity waveform of the movement of conveying of saidflasks on said conveying line such that the modified velocity waveformdoes not include the first and second natural frequencies calculated bysaid first and second natural frequency-calculation means; andinstructing means for providing operating instructions to said electricpusher-cylinder, said electric cushion-cylinder, and said automaticpouring device, based on said modified velocity waveform.
 3. A method ofsuppressing sloshing in a casting line, wherein said casting lineincludes: a conveying line in which an electric pusher-cylinder islocated at one end of the conveying line for intermittently pushing outa plurality of flasks, wherein each flask contains a mold, one by one,and an electric cushion-cylinder is located at the other end of saidconveying line and is opposed to said electric pusher-cylinder toreceive and cushion a group of said pushed flasks such that saidconveying line conveys said plurality of flasks and is arranged linearlybetween said electric pusher-cylinder and said electriccushion-cylinder; an automatic pouring device that has a ladle forcontaining molten metal and that can be moved in synchronization withthe flask on the conveying line, to pour the molten metal into the moldby tilting said ladle; driving means for driving said electricpusher-cylinder, said electric cushion-cylinder, and said automaticpouring device along a conveyed direction of said flasks; controllingmeans for controlling said driving means; and instructing means forproviding operating instructions for said electric pusher-cylinder, saidelectric cushion-cylinder, and said automatic pouring device to saiddriving means through said controlling means wherein; said methodcontrols said casting line using a controller having filtering means,based on a feedforward control program such that the sloshing thatoccurs in the molten metal is suppressed when said ladle and said moldmove by a distance corresponding to one flask, said method comprising:calculating a first natural frequency of the molten metal in said ladlebased on a predetermined relationship between the weight and the naturalfrequency for the molten metal in said ladle, and the measured weight ofthe molten metal in said ladle, and calculating a second naturalfrequency of the molten metal in said mold based on a predeterminedrelationship between the weight and the natural frequency for the moltenmetal in said mold, and the measured weight of the molten metal in saidmold; under the first natural frequency, the second natural frequency,and the parameters of said controlling means that are preliminarilycalculated such that they do not exceed the capacities of said drivingmeans and are stored, removing components that are located near thefirst and second frequencies from the operating instructions, in whichthe maximum value of at least one of a velocity of the movement, anacceleration of the movement, and a jerk of the movement of said ladleand said mold is restricted, by said filtering means using said storedparameters, wherein said components to be removed are decided based on asimulation using a model representing the characteristics of saidcasting line to repeatedly calculate said component by the followingequation (1) or (2), $\begin{matrix}{{{y(t)} = {{{b_{0}(f)}{x(t)}} + {{b_{1}(f)}{x( {t - 1} )}} + {{b_{2}(f)}{x( {t - 2} )}} + \ldots - {{a_{1}(f)}{y( {t - 1} )}} - {{a_{2}(f)}{y( {t - 2} )}} - \ldots}}{{y(t)} = {{\sum\limits_{j = 0}^{m}\; {{b_{j}(f)}{x( {t - j} )}}} - {\sum\limits_{i = 1}^{n}\; {{a_{1}(f)}{y( {t - i} )}}}}}} & (1) \\\begin{matrix}{{F(S)} = \frac{Y(S)}{X(S)}} \\{= \frac{{{b_{0}(f)}S^{0}} + {{b_{1}(f)}S^{1}} + {{b_{2}(f)}S^{2}} + \ldots}{{{a_{0}(f)}S^{0}} + {{a_{1}(f)}S^{1}} + {{a_{2}(f)}S^{2}} + \ldots}} \\{= \frac{\sum\limits_{j = 0}^{m}\; {{b_{j}(f)}S^{j}}}{\sum\limits_{i = 0}^{n}\; {{a_{i}(f)}S^{i}}}}\end{matrix} & (2)\end{matrix}$ while gradually varying filtering parameters ai(f), bj(f)that are parameterized by a resonance frequency f that are successivelycalculated from the molten metal in said ladle and said mold, wherein y(t-i) is time-series data that are output before i controlling cycles,x(t-j) is time-series data that are input before j controlling cycles, Sis the Laplace operator, and equation (1) can be derived by applying a Ztransformation to the transfer function of the filter that is expressedas equation (2); and entering the operating instructions, in which saidcomponents that are located near the first and second frequencies havebeen removed, in said controlling means based on only said feedforwardcontrolling program, to operate said driving means based on only saidfeedforward controlling program without using a feedback controlprogram.
 4. A system for the suppression of sloshing in a casting line,wherein said casting line includes: a conveying line in which anelectric pusher-cylinder is located at one end of the conveying line forintermittently pushing out a plurality of flasks that each contain amold, one by one, and an electric cushion-cylinder is located at theother end of said conveying line and is opposed to said electricpusher-cylinder to receive and cushion a group of said pushed flaskssuch that said conveying line conveys said plurality of flasks and isarranged linearly between said electric pusher-cylinder and saidelectric cushion-cylinder; an automatic pouring device that has a ladlefor containing molten metal and that can be moved in synchronizationwith the flask on the conveying line, to pour the molten metal into themold by tilting said ladle; driving means for driving said electricpusher-cylinder, said electric cushion-cylinder, and said automaticpouring device along a conveyed direction of said flasks; andcontrolling means for controlling said driving means; wherein saidsystem controls said casting line to suppress the sloshing that occursin the molten metal in said ladle and the mold when said ladle and saidmold move by a distance corresponding to one flask, said systemcomprising: a first weight-calculation means for calculating the weightof the molten metal in said ladle; a second weight-calculation means forcalculating a second natural frequency of the molten metal in said mold;a first natural frequency-calculation means for calculating a firstnatural frequency based on a predetermined relationship between theweight and the natural frequency for the molten metal in said ladle, andthe calculated weight of the molten metal in said ladle by said firstweight-calculation means; a second natural frequency-calculation meansfor calculating a second natural frequency based on a predeterminedrelationship between the weight and the natural frequency for the moltenmetal in said mold, and the calculated weight of the molten metal insaid mold by said second weight-calculation means; instructing means forproviding operating instructions based on a feedforward program foroperations of said electric pusher-cylinder, said electriccushion-cylinder, and said automatic pouring device, to said drivingmeans through said controlling means; parameter calculation means forpreliminarily calculating the parameters of said controlling means suchthat the calculated parameters do not exceed the capacity of saiddriving means; storing means for receiving and storing the calculatedparameters from said parameter calculation means; restriction means forrestricting a maximum value of at least one of a velocity of themovement, an acceleration of the movement, and a jerk of the movement ofsaid automatic pouring device and said mold; filtering means forreceiving the first and second resonance frequencies from said first andsecond frequency-calculation means, and for removing components that arelocated near the first and second frequencies from the operatinginstructions, in which the maximum value is restricted by saidrestriction means, using the stored parameters from the stored means,wherein said components to be removed are decided based on a simulationusing a model representing the characteristics of said casting line torepeatedly calculate said component, under said stored parameters, bythe following equation (1) or (2), $\begin{matrix}{{{y(t)} = {{{b_{0}(f)}{x(t)}} + {{b_{1}(f)}{x( {t - 1} )}} + {{b_{2}(f)}{x( {t - 2} )}} + \ldots - {{a_{1}(f)}{y( {t - 1} )}} - {{a_{2}(f)}{y( {t - 2} )}} - \ldots}}{{y(t)} = {{\sum\limits_{j = 0}^{m}\; {{b_{j}(f)}{x( {t - j} )}}} - {\sum\limits_{i = 1}^{n}\; {{a_{1}(f)}{y( {t - i} )}}}}}} & (1) \\\begin{matrix}{{F(S)} = \frac{Y(S)}{X(S)}} \\{= \frac{{{b_{0}(f)}S^{0}} + {{b_{1}(f)}S^{1}} + {{b_{2}(f)}S^{2}} + \ldots}{{{a_{0}(f)}S^{0}} + {{a_{1}(f)}S^{1}} + {{a_{2}(f)}S^{2}} + \ldots}} \\{= \frac{\sum\limits_{j = 0}^{m}\; {{b_{j}(f)}S^{j}}}{\sum\limits_{i = 0}^{n}\; {{a_{i}(f)}S^{i}}}}\end{matrix} & (2)\end{matrix}$ while gradually varying filtering parameters ai(f), bj(f)that are parameterized by a resonance frequency f that are successivelycalculated from the molten metal in said ladle and said mold, wherein y(t-i) is time-series data that are output before i controlling cycles,x(t-j) is time-series data that are input before j controlling cycles, Sis the Laplace operator, and equation (1) can be derived by applying a 2transformation to the transfer function of the filter that is expressedas equation (2); and wherein said instructing means provides saidcontrolling means with operating instructions in which said componentsthat are located near the first and second frequencies have been removedsuch that said controlling means carries out the controls based on onlysaid feedforward controlling program without using a feedback controlprogram.
 5. A computer readable media storing a computer program for thesuppression of sloshing in a casting line, wherein said casting lineincludes: a conveying line in which an electric pusher-cylinder islocated at one end of the conveying line for intermittently pushing outa plurality of flasks that each contain a mold, one by one, and anelectric cushion-cylinder is located at the other end of said conveyingline and is opposed to said electric pusher-cylinder to receive andcushion a group of said pushed flasks such that said conveying lineconveys said plurality of flasks and is arranged linearly between saidelectric pusher-cylinder and said electric cushion-cylinder; and anautomatic pouring device that has a ladle for containing molten metaland that can be moved in synchronization with the flask on the conveyingline, to pour the molten metal into the mold by tilting said ladle;wherein said computer program causes a computer having filter means tocontrol said electric pusher-cylinder and said electric cushion-cylindersuch that the sloshing that occurs in the molten metal is suppressedwhen said ladle and said mold move by a distance corresponding to oneflask, said computer program comprising the steps to be executed by saidcomputer of: calculating a first natural frequency of the molten metalin said ladle based on a predetermined relationship between the weightand the natural frequency for the molten metal in said ladle, and themeasured weight of the molten metal in said ladle, and calculating asecond natural frequency of the molten metal in said mold based on apredetermined relationship between the weight and the natural frequencyfor the molten metal in said mold, and the measured weight of the moltenmetal in said mold; entering the first and second natural frequencies insaid filtering means to modify a velocity waveform of the movement ofconveying of said flasks such that the modified velocity waveform doesnot include the first and second natural frequencies; and driving saidelectric pusher-cylinder and said electric cushion-cylinder such thatthe velocity waveform of the movement of conveying of said flasks issaid modified velocity waveform.
 6. A computer readable media storing acomputer program for the suppression of sloshing in a casting line,wherein said casting line includes: a conveying line in which anelectric pusher-cylinder is located at one end of the conveying line forintermittently pushing out a plurality of flasks that each contain amold, one by one, and an electric cushion-cylinder is located at theother end of said conveying line and is opposed to said electricpusher-cylinder to receive and cushion a group of said pushed flaskssuch that said conveying line that conveys said plurality of flasks isarranged linearly between said electric pusher-cylinder and saidelectric cushion-cylinder; an automatic pouring device that has a ladlefor containing molten metal and that can be moved in synchronizationwith the flask on the conveying line, to pour the molten metal into themold by tilting said ladle; driving means for driving said electricpusher-cylinder, said electric cushion-cylinder, and said automaticpouring device along a conveyed direction of said flasks; controllingmeans for controlling said driving means; and instructing means forproviding operating instructions for said electric pusher-cylinder, saidelectric cushion-cylinder, and said automatic pouring device to saiddriving means through said controlling means; wherein said computerprogram causes a computer having filter means to control said electricpusher-cylinder and said electric cushion-cylinder such that thesloshing that occurs in the molten metal is suppressed when said ladleand said mold move by a distance corresponding to one flask, saidcomputer program comprising the steps to be executed by said computerof: calculating a first natural frequency of the molten metal in saidladle based on a predetermined relationship between the weight and thenatural frequency for the molten metal in said ladle, and the measuredweight of the molten metal in said ladle, and calculating a secondnatural frequency of the molten metal in said mold based on apredetermined relationship between the weight and the natural frequencyfor the molten metal in said mold, and the measured weight of the moltenmetal in said mold; under the first natural frequency, the secondnatural frequency, and parameters of said controlling means that arepreliminarily calculated such that they do not exceed capacities of saiddriving means and are stored, removing components that are located nearthe first and second frequencies from the operating instructions, inwhich at least one of a velocity of the movement, an acceleration of themovement, and a jerk of the movement of said ladle and said mold, bysaid filtering means using said stored parameters, wherein saidcomponents to be removed are decided based on a simulation using a modelrepresenting characteristics of said casting line to repeatedlycalculate said components by the following equation (1) or (2),$\begin{matrix}{{{y(t)} = {{{b_{0}(f)}{x(t)}} + {{b_{1}(f)}{x( {t - 1} )}} + {{b_{2}(f)}{x( {t - 2} )}} + \ldots - {{a_{1}(f)}{y( {t - 1} )}} - {{a_{2}(f)}{y( {t - 2} )}} - \ldots}}{{y(t)} = {{\sum\limits_{j = 0}^{m}\; {{b_{j}(f)}{x( {t - j} )}}} - {\sum\limits_{i = 1}^{n}\; {{a_{1}(f)}{y( {t - i} )}}}}}} & (1) \\\begin{matrix}{{F(S)} = \frac{Y(S)}{X(S)}} \\{= \frac{{{b_{0}(f)}S^{0}} + {{b_{1}(f)}S^{1}} + {{b_{2}(f)}S^{2}} + \ldots}{{{a_{0}(f)}S^{0}} + {{a_{1}(f)}S^{1}} + {{a_{2}(f)}S^{2}} + \ldots}} \\{= \frac{\sum\limits_{j = 0}^{m}\; {{b_{j}(f)}S^{j}}}{\sum\limits_{i = 0}^{n}\; {{a_{i}(f)}S^{i}}}}\end{matrix} & (2)\end{matrix}$ while gradually varying filtering parameters ai(f), bj(f)that are parameterized by a resonance frequency f that are successivelycalculated from the molten metal in said ladle and said mold, wherein y(t-i) is time-series data that are output before i controlling cycles,x(t-j) is time-series data that are input before j controlling cycles, Sis the Laplace operator, and equation (1) can be derived by applying a Ztransformation to the transfer function of the filter that is expressedas equation (2); and entering the operating instructions, in which saidcomponents located near the first and second frequencies have beenremoved, in said controlling means based on only said feedforwardcontrolling program, to operate said driving means based on only saidfeedforward controlling program without using a feedback controlprogram.